Abstract
Aggregates are used to compute single pieces of information from separate data items, such as records in a database or answers to a query to a logic program. The maximum and minimum are well-known examples of aggregates. The computation of aggregates in Prolog or variant-based tabling can loop even if the aggregate at hand can be finitely determined. When answer subsumption or mode-directed tabling is used, termination improves, but the behavior observed in existing proposals is not consistent. We present a framework to incrementally compute aggregates for elements in a lattice. We use the entailment and join relations of the lattice to define (and compute) aggregates and decide whether some atom is compatible with (entails) the aggregate. The semantics of the aggregates defined in this way is consistent with the LFP semantics of tabling with constraints. Our implementation is based on the TCLP framework available in Ciao Prolog, and improves its termination properties w.r.t. similar approaches. Defining aggregates that do not fit into the lattice structure is possible, but some properties guaranteed by the lattice may not hold. However, the flexibility provided by this possibility justifies its inclusion. We validate our design with several examples and we evaluate their performance.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
This definition would usually be based on a set instead of a multiset. The reason to choose explicitly a multiset will be clear in Sect. 4.5, when we apply our implementation to operations that cannot be embedded in a lattice.
- 2.
The original example used max. For coherence with the rest of the cases in this paper, we have converted it to use min.
- 3.
Batch scheduling returns answers as soon as they are found.
- 4.
Stable versions of Ciao Prolog are available at http://www.ciao-lang.org. However, ATCLP is still in development and not fully available yet in the stable versions.
References
Arias, J., Carro, M.: Description and evaluation of a generic design to integrate CLP and tabled execution. In: International Symposium on Principles and Practice of Declarative Programming, pp. 10–23. ACM, September 2016
Arias, J., Carro, M.: Description, implementation, and evaluation of a generic design for tabled CLP. Theory and Practice of Logic Programming (2018) (to appear)
Bratko, I.: Prolog Programming for Artificial Intelligence. Pearson Education, London (2001)
Chico de Guzmán, P., Carro, M., Hermenegildo, M.V., Stuckey, P.: A general implementation framework for tabled CLP. In: Schrijvers, T., Thiemann, P. (eds.) FLOPS 2012. LNCS, vol. 7294, pp. 104–119. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29822-6_11
Cui, B., Warren, D.S.: A system for tabled constraint logic programming. In: Lloyd, J., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Palamidessi, C., Pereira, L.M., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 478–492. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44957-4_32
Guo, H.F., Gupta, G.: Simplifying dynamic programming via mode-directed tabling. Softw. Pract. Exp. 1, 75–94 (2008)
Holzbaur, C.: Metastructures vs. attributed variables in the context of extensible unification. In: Bruynooghe, M., Wirsing, M. (eds.) PLILP 1992. LNCS, vol. 631, pp. 260–268. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-55844-6_141
Kemp, D.B., Stuckey, P.J.: Semantics of logic programs with aggregates. In: Saraswat, V.A., Ueda, K. (eds.) International Symposium on Logic Programming, pp. 387–401. October 1991
Pelov, N., Denecker, M., Bruynooghe, M.: Well-founded and stable semantics of logic programs with aggregates. Theory Pract. Log. Program. 3, 301–353 (2007)
Picard, G.: Artificial intelligence - implementing minimax with prolog. https://www.emse.fr/~picard/cours/ai/minimax/
Santos Costa, V., Rocha, R., Damas, L.: The YAP prolog system. Theory Pract. Log. Program. 1–2, 5–34 (2012)
Schrijvers, T., Demoen, B., Warren, D.S.: TCHR: a Framework for tabled CLP. Theory Pract. Log. Program. 4, 491–526 (2008)
Swift, T., Warren, D.S.: Tabling with answer subsumption: implementation, applications and performance. In: Janhunen, T., Niemelä, I. (eds.) JELIA 2010. LNCS (LNAI), vol. 6341, pp. 300–312. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15675-5_26
Swift, T., Warren, D.S.: XSB: extending prolog with tabled logic programming. Theory Pract. Log. Program. 1–2, 157–187 (2012)
Vandenbroucke, A., Pirog, M., Desouter, B., Schrijvers, T.: Tabling with sound answer subsumption. Theory Pract. Log. Program. 16(5–6), 933–949 (2016). 32nd International Conference on Logic Programming
Zhou, N.F.: The language features and architecture of B-Prolog. Theory Pract. Log. Program. 1–2, 189–218 (2012)
Zhou, N.F., Kameya, Y., Sato, T.: Mode-directed tabling for dynamic programming, machine learning, and constraint solving. In: International Conference on Tools with Artificial Intelligence, No. 2, pp. 213–218. IEEE, October 2010
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Arias, J., Carro, M. (2019). Incremental Evaluation of Lattice-Based Aggregates in Logic Programming Using Modular TCLP. In: Alferes, J., Johansson, M. (eds) Practical Aspects of Declarative Languages. PADL 2019. Lecture Notes in Computer Science(), vol 11372. Springer, Cham. https://doi.org/10.1007/978-3-030-05998-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-05998-9_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-05997-2
Online ISBN: 978-3-030-05998-9
eBook Packages: Computer ScienceComputer Science (R0)